Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.2 - Applications of Propositional Logic - Exercises - Page 24: 39

Answer

1 senator is honest, 49 are corrupt

Work Step by Step

We know at least one senator is honest. Lets assume 2 senators are honest. If 2 senators are honest, the statement "given any two Freedonian senators, at least one is corrupt" is not true for those 2 honest senators. Therefore, 1 senator is honest and 49 are corrupt.
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